Lesson 2 Do You See What I See? Develop Understanding

Ready

Consider the given statements and fill in the blank with something that makes sense. The first comparison demonstrates a relationship and the second comparison has a blank for you to fill in based on the relationship provided. There may be more than one logical way to fill in the blank.

For example, in the statement, “Foot is to boot as hand is to .” You would consider the first part of the statement “foot is to boot” and think about the relationship. It is apparent that a foot can go in or wear a boot. Logically then it would make sense to fill in the blank with “glove” since a hand can go in or wear a glove.

1.

Pencil is to writing as violin is to

2.

Fishing is to lake as soccer is to

3.

Equal slopes is to parallel lines as negative reciprocal slopes is to

4.

Hexagon is to triangle as decagon is to

5.

Subtraction is to addition as division is to

6.

Congruent is to shapes as equal is to

Decide if the following statements provide a true logical conclusion or if the statement is false. If false, provide a counterexample.

7.

An acute triangle only needs to have one acute angle.

8.

If a rectangle is cut in half then there will be two triangles.

9.

If you have supplementary angles, they will create a straight line.

10.

If you have complementary angles, they will add up to $90 °$ .

Set

Many diagrams have a history and progression to the way they are created. For each diagram, list the steps in the order that you think they occurred to make the diagram. Then make a conjecture about the piece of the diagram indicated. Consider using a compass and straightedge to reconstruct the diagram as you work. Finally, write an argument that can be used to justify to someone that your conjecture would be true.

11.

Diagram

List the steps to create the diagram:

Conjecture about quadrilateral $A C E D$ :

Justification:

12.

Diagram:

List of steps to create the diagram:

Conjecture about quadrilateral $A B C D$ :

Justification:

Examine the diagram and add any information that is given to the diagram. Make a plan for finding the value of $x$ . Follow your plan. Show your work, justifying the results.

13.

Given: $m ∠ C = 90 °$

$x =$

14.

Given: $m ∠ A B C = 90 °$

$x =$

15.

Given: $△ B E C$ , $△ C E D$ , and $△ D A B$ are right triangles.

$x =$

Go

16.

Label points $C$ , $E$ , and $D$ with the correct ordered pairs.
Translate $△ C E D$ down $4$ and right $6$ . Label the image as $△ C^{'} E^{'} D^{'}$ and include the new ordered pairs.
Draw $\overset{―}{C C^{'}}$ , $\overset{―}{E E^{'}}$ , and $\overset{―}{D D^{'}}$ . What is the slope of each of these line segments?
Reflect $△ C^{'} E^{'} D^{'}$ across the $y = 0$ line. Label the image $△ C^{″} E^{″} D^{″}$ . Include the new ordered pairs.
Draw $\overset{―}{C^{'} C^{″}}$ and $\overset{―}{E^{'} E^{″}}$ . Why don’t you need to draw $\overset{―}{D^{'} D^{″}}$ ? What is the relationship between $\overset{―}{C^{'} C^{″}}$ and $\overset{―}{E^{'} E^{″}}$ to the $y = 0$ line?
Rotate $△ C E D$ $180 °$ about the point $(- 2, 0)$ . Label the image $△ C^{‴} E^{‴} D^{‴}$ . Include the new ordered pairs.